Transient Thermal Response Transient Models Lumped Tenbroek 1997

Transient Thermal Response • Transient Models – Lumped: Tenbroek (1997), Rinaldi (2001), Lin (2004) – Introduce CTH usually with approximate Green’s functions; heated volume is a function of time (Joy, 1970) Instantaneous T rise Due to very sharp heating pulse t ‹‹ V 2/3/ – Finite-Element methods More general Simplest (~ bulk Si FET) Temperature evolution anywhere (r, t) due to arbitrary heating function P(0<t’<t) inside volume V (d. V’ V) (Joy 1970) Temperature evolution of a step-heated point source into silicon half-plane (Mautry 1990) © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 1

Instantaneous Temperature Rise L d W Instantaneous T rise Due to very sharp heating pulse t ‹‹ V 2/3/ • Neglect convection & radiation • Assuming lumped body • Biot = h. L/k << 1, internal resistance and T variation neglected, T(x) = T = const. © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 2

Lumped Temperature Decay L W d T(t=0) = TH T decay • After power input switched off • Assuming lumped body • RTH = 1/h. A • CTH = c. V • Time constant ~ RTHCTH © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 3

Electrical and Mechanical Analogy • Thermal capacitance (C = ρc. V) normally spread over the volume of the body • When Biot << 1 we can lump capacitance into a single “circuit element” (electrical or mechanical analogy) There are no physical elements analogous to mass or inductance in thermal systems © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 4

Transient Edge (Face) Heating When is only the surface of a body heated? I. e. when is the depth dimension “infinite”? Note: Only heated surface B. C. is available Lienhard book, http: //web. mit. edu/lienhard/www/ahtt. html Also http: //www. uh. edu/engines/epi 1384. htm © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 5

Transient Heating with Convective B. C. • If body is “semi-infinite” there is no length scale on which to build the Biot number • Replace Biot (αt)1/2 Note this reduces to previous slide’s simpler expression (erf only) when h=0! © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 6

Transient Lumped Spreading Resistance Source: Timo Veijola, http: //www. aplac. hut. fi/publications/bec-1996 -01/bec. html • Point source of heat in material with k, c and α = k/c • Or spherical heat source, outside sphere ~ Bulk Si FET transient Temperature evolution of a step-heated point source into silicon half-plane (Mautry 1990) • This is OK if we want to roughly approximate transistor as a sphere embedded in material with k, c Characteristic diffusion length LD = (αt)1/2 © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 7

Transient of a Step-Heated Transistor In general: Carslaw and Jaeger (2 e, 1986) © 2010 Eric Pop, UIUC “Instantaneously” means short pulse time vs. Si diffusion time (t < LD 2/α) or short depth vs. Si diffusion length (L < (αt)1/2) ECE 598 EP: Hot Chips 8

Device Thermal Transients (3 D) © 2010 Eric Pop, UIUC ECE 598 EP: Hot

Temperature of Pulsed Diode Holway, TED 27, 433 (1980) © 2010 Eric Pop, UIUC

Interconnect Reliability © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 11

Transient of a Step-Heated Interconnect When to use “adiabatic approximation” and when to worry

Transient Thermal Failure © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 13

Understanding the sqrt(t) Dependence • Physical = think of the heated volume as it

Time Scales of Thermal Device Failure • Three time scales: – “Small” failure times: all heat dissipated within defect, little heat lost to surrounding ~ adiabatic (ΔT ~ Pt) – Intermediate time: heating up surrounding layer of (αt)1/2 – “Long” failure time ~ steady-state, thermal equilibrium established: ΔT ~ P*const. = PRTH © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 15

Ex: Failure of Si. Ge HBT and Cu IC Wunsch-Bell curve of HBT ©

Ex: Failure of Al/Cu Interconnects Banerjee et al. , IRPS 2000 Ju & Goodson, Elec. Dev. Lett. 18, 512 (1997) • Fracture due to the expansion of critical volume of molten Al/Cu. (@ 1000 0 C) © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 17

Temperature Rise in Vias S. Im, K. Banerjee, and K. E. Goodson, IRPS 2002 Via and interconnect dimensions are not consistent from a heat generation / thermal resistance perspective, leading to hotspots. New model accounts for via conduction and Joule heating and recommends dimensions considering temperature and EM lifetime. Based on ITRS global lines of a 100 nm technology node (Left: ANSYS simulation. Right: Closed-Form Modeling) © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 18

Time Scales of Electrothermal Processes Source: K. Goodson © 2010 Eric Pop, UIUC ECE

ESD: Electrostatic Discharge J. Vinson & J. Liou, Proc. IEEE 86, 2 (1998) •

Common ESD Models Gate J. Vinson & J. Liou, Proc. IEEE 86, 2 (1998) Source Drain Combined, transient, electro-thermal device models Lumped: Human-Body Model (HBM) Lumped: Machine Model (MM) © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 21

Reliability Source: M. Stan • The Arrhenius Equation: MTF=A*exp(Ea/k. BT) • • • MTF: mean time to failure at T A: empirical constant Ea: activation energy k. B: Boltzmann’s constant T: absolute temperature Ea = 1. 1 e. V Ea = 0. 7 e. V • Failure mechanisms: • • • Die metalization (Corrosion, Electromigration, Contact spiking) Oxide (charge trapping, gate oxide breakdown, hot electrons) Device (ionic contamination, second breakdown, surface-charge) Die attach (fracture, thermal breakdown, adhesion fatigue) Interconnect (wirebond failure, flip-chip joint failure) Package (cracking, whisker and dendritic growth, lid seal failure) • Most of the above increase with T (Arrhenius) • Notable exception: hot electrons are worse at low temperatures © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 22

Improved Reliability Analysis M. Stan (2007), Van der Bosch, IEDM (2006) • There is NO “one size fits all” reliability estimate approach • Typical reliability lifetime estimates done at worst-case temperature (e. g. 125 o. C) which is an OVERDESIGN life consumption rate © 2010 Eric Pop, UIUC • Apply in a “lumped” fashion at the granularity of microarchitecture units ECE 598 EP: Hot Chips 23

Combined Package Model Steady-state: Tj – junction temperature Tc – case temperature Ts –

Thermal Design Summary • Temperature affects performance, power, and reliability • Architecture-level: conduction only – Very crude approximation of convection as equivalent resistance – Convection, in general: too complicated, need CFD! • • Use compact models for package Power density is key Temporal, spatial variation are key Hot spots drive thermal design © 2010 Eric Pop, UIUC ECE 598 EP: Hot Chips 25